On p-adic families of automorphic forms
On p-adic families of automorphic forms
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关于自守形式的 p-adic 族
DOI：
10.1007/978-3-0348-7919-4_2
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发表时间：
2004
影响因子：
1.9
通讯作者：
Kevin Buzzard
中科院分区：
文献类型：
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作者：
Kevin Buzzard
Coleman和Mazur构造了“特征曲线”，几何对象参数化了某些超收敛的p进模形式。我们给出了另外两类约化群的超收敛p进自同构形式的定义——首先是数域上的GLI，其次是有理数上的确定四元代数dx， D。我们给出了几个理由，为什么我们相信我们构造的对象是在这种情况下超收敛p进模形式的正确模拟。
Coleman and Mazur have constructed “eigencurves”, geometric objects parametrising certain overconvergent p-adic modular forms. We formulate definitions of overconvergent p-adic automorphic forms for two more classes of reductive groups — firstly for GLI over a number field, and secondly for D x , D a definite quaternion algebra over the rationals. We give several reasons why we believe the objects we construct to be the correct analogue of an overconvergent p-adic modular form in this setting.